Lattice theory of polymer blends and liquid mixtures: Beyond the Flory–Huggins approximation

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Abstract
Lattice model calculations of corrections to the Flory–Huggins mean field approximation from the preceding paper are applied to the thermodynamic properties of polymer blends. We describe the variation of the noncombinatorial entropy of mixing with composition and monomer structure by considering an extended lattice model in which monomers extend over several lattice sites and therefore have differing sizes and shapes. Composition and temperature dependences of heats of mixing or the equivalent Flory χ parameters are in accord with the magnitude observed experimentally. It is only because we treat the idealized limit of an incompressible blend, for simplicity, that the heat of mixing and Flory χ parameter depend on one effective interaction parameter that is represented in terms of differences in van der Waals energies. The corrections to the Flory–Huggins approximation produce a much lower critical temperature in general agreement with recent Monte Carlo simulations by Sariban and Binder. Concentrated polymer solutions and mixtures of small flexible molecules follow as simple limits of the blend theory and are used to compute the surface volume fractions that appear as empirical parameters into previous theories of liquid mixtures. Comments are made concerning recent observations of a cross link dependence of the Flory χ parameters for slightly swollen polymer networks.